Question

find the answer of the given question

Answer 1

Let the speed of A and B be x km/hr & y km/hr
Time taken by A to cover 30 km =  D/S =30/x hrs.
Time taken by B to cover 30 km =  D/S = 30/y hrs.
30/x - 30/y = 3
10/x - 10/y = 1.......(i)
if A doubles his pace,then the speed of A is 2x km/hr.
& time taken by A to cover 30 km = 30/2x hrs.
& time taken by B to cover 30 km = 30/y hrs.

30/y - 30/2x = 3/2
10/y - 10/2x   = 1/2
-10/x + 20/y = 1..........(2)

Let  1/x = u and 1/y = v
putting the value in eq. 1 and 2
10u - 10 v = 1........(3)
-10u + 20 v = 1 .......(4)


On adding eq.3 and 4, we get
10v=2
v = 1/5
put v = 1/5 in eq.3, we get
10u - 2= 1

10u = 1+2

10u = 3

u = 3/10
now, u = 3/10 = 1/x
x = 10/3.
and v = 1/5 = 1/y
y = 5

speed of A and B are 10/3 km/hr and 5 km/hr respectively.